A2.F.1.8 Graph piecewise functions with no more than three branches (including linear, quadratic, or exponential branches) and analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant.
In a Nutshell
Students graph and analyze piecewise functions and also identify critical points and intervals of increase or decrease.
Student Actions

Teacher Actions


Students will develop a productive mathematical disposition that piecewise functions are sensible, useful and worthwhile in representing realworld situations.

Students will develop a deep conceptual understanding of piecewise functions as different functions together as one unit with different domain and range.

Students will develop accurate and appropriate procedural fluency for graphing piecewise functions.
 Students will develop deep and flexible conceptual understanding of critical points and key characteristics of a piecewise function by analyzing a given a graph.


Focus studentsâ€™ attention on the structure and/or essential features of piecewise functions.

Ask questions that go beyond simply producing a graph to probing thinking and requiring explanation.

Provide students with opportunities through a variety of activities to practice of graphing piecewise functions.

Provide students with opportunities to use their own reasoning, strategies and methods for graphing and interpreting piecewise functions. Allow students time to collaborate, discuss and defend their reasoning, strategies, and methods.

Allow students time to discover real world problems that are represented by piecewise functions. Give students choice on how to present their findings.

Key Understandings

Misconceptions



OKMath Framework Introduction
Algebra 2 Grade Introduction
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